12x12 Queens Puzzle #177
Difficulty: medium. Place 12 queens on this 12x12 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 18-step reasoning is written out below.
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Step-by-step solution for puzzle #177
What follows is a complete solve of puzzle #177, worked the way a person works it rather than the way a computer does. It runs to 18 deductions — 12 queen placements and 6 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the region shadow.
Techniques this board needs: last square in a region, region confined to one line, region shadow.
Show the full walkthrough (11 steps) — contains the solution
Step 1. Only row 10, column 4 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 4, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 2. All of the slate region's remaining squares (2 open squares) lie in column 1. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.
Step 3. Khaki cannot leave column 12 — every one of its open squares (5 open squares) sits there. That column belongs to khaki, so every square in it owned by another colour is dead: 6 squares in all.
Step 4. All of the amber region's remaining squares (2 open squares) lie in column 11. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 11 squares come off.
The board after step 4 — 1 of 12 queens placed. Step 5. Mint cannot leave column 10 — every one of its open squares (2 open squares) sits there. That column belongs to mint, so every square in it owned by another colour is dead: 9 squares in all.
Step 6. The teal region has 4 squares left, spread across rows 11 and 12, columns 7–9. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 7. Only row 12, column 9 is still open in rose, and since each colour must take a queen, that settles it. Everything else in row 12, in column 9, in rose and in the ring around that square is now dead.
The board after step 7 — 2 of 12 queens placed. Step 8. The teal region is down to one open square, at row 11, column 7. Every colour holds exactly one queen, so that square is forced. Row 11 and column 7 are now spoken for, along with the squares touching that queen.
Step 9. Only row 9, column 6 is still open in orange, and since each colour must take a queen, that settles it. That clears row 9, column 6, the rest of the orange region and every square adjacent to it — diagonals included.
Step 10. All of the red region's remaining squares (6 open squares) lie in column 8. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 11. From here the board cascades. Keep alternating the region sweep and the line sweep and 8 queens fall out in order without any new idea being needed: indigo has one square left, so its queen takes row 1, column 5; amber has one square left, so its queen takes row 2, column 11; mint has one square left, so its queen takes row 4, column 10; pale yellow has one square left, so its queen takes row 7, column 2; slate has one square left, so its queen takes row 5, column 1; blue has one square left, so its queen takes row 3, column 3; khaki has one square left, so its queen takes row 8, column 12; red has one square left, so its queen takes row 6, column 8. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 6, column 8.
The board after step 11 — 12 of 12 queens placed.
That completes the board: 12 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 12x12 Queens puzzle #177
Puzzle #177 is one of the medium-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
Puzzle #177 has been checked to admit exactly one arrangement of queens, and every step toward it is deducible from what is already on the board. There is no point at which you are expected to pick a square and hope. The only thing that differs between boards is how quickly the first certainty surfaces, and that depends entirely on the shapes the colors happen to take here.
How the colors divide this board
From smallest to largest, the regions on puzzle #177 are: sea green (1 square), slate (2 squares), mint (4 squares), teal (5 squares), rose (6 squares), khaki (7 squares), amber (8 squares), indigo (14 squares), orange (14 squares), pale yellow (25 squares), blue (28 squares), red (30 squares). An even split would hand every color 12 squares, so the sea green region is running 11 squares under that average while the red region is the roomiest area on the grid with 30 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So sea green, with 1 square, is under far more pressure than red with 30. A 29-square gap like this one rewards players who start where the choices are fewest.
Square count is only half the story — how a color is arranged counts too. Mint is the tidiest shape on #177, packing 100% of its 2×2 bounding box, whereas orange straggles across its 7×4 box at just 50%. Tidy blocks are easy to work around; scattered ones touch more lines and resist resolution.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a medium board.
Sea green: 1 square across rows 10–10, columns 4–4. It never leaves row 10, so its queen is locked to that row.
Slate covers 2 squares, spanning 2 rows and 1 column (rows 5–6, columns 1–1). It sits wholly inside column 1, so its queen must be in that column.
Mint occupies 4 squares within rows 3–4, columns 10–11.
Teal: 5 squares across rows 10–12, columns 7–9.
Rose covers 6 squares, spanning 2 rows and 4 columns (rows 11–12, columns 8–11).
Khaki occupies 7 squares within rows 7–12, columns 11–12.
Amber: 8 squares across rows 1–6, columns 11–12.
Indigo covers 14 squares, spanning 3 rows and 7 columns (rows 1–3, columns 4–10).
Orange occupies 14 squares within rows 6–12, columns 4–7.
Pale yellow: 25 squares across rows 6–12, columns 1–6.
Blue covers 28 squares, spanning 8 rows and 6 columns (rows 1–8, columns 1–6).
Red occupies 30 squares within rows 3–10, columns 6–11.
Where to start on this board
Open on the tightest color. Here that is sea green, confined to 1 square between rows 10 and 10 and columns 4 and 4. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #177.
Because sea green never leaves row 10, its queen must be in that row — and that instantly settles row 10 for everyone else. Sweep along it and X out every square that is not sea green. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Mint, slate and rose are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.
The tightest lines on puzzle #177
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 1 and 2 are the narrowest, touched by only 3 colors. Columns 2, 3 and 12 are the tightest columns, with 2 colors.
The fewer colors a line touches, the sooner it surrenders its queen. A row meeting just 3 colors has to be claimed by one of them, which pushes every remaining region into the other 11 rows. Row 10, meeting 6 colors, is the opposite case — the busiest line on #177 and the last one you should expect to crack.
Working through the middle game
Once two or three queens are down, the board changes character. Each queen removes an entire row, an entire column and the ring of up to eight squares around it, so the grid shrinks faster than most people expect. The habit that pays here is marking rather than remembering: after every placement, cross out the full row, the full column and all eight neighbours before hunting for the next move.
The whole middle game reduces to two sweeps. Sweep the twelve colors looking for one with a single square left; sweep the twelve rows and twelve columns looking for the same. Each sweep feeds the next, and switching between them deliberately — rather than drifting — is what separates a fast 12x12 solve from a stalled one.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #177 is rated medium
The medium label comes out of four measurable things about #177: three of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 3 colors, and its largest and smallest regions differ by 29. Boards that score tight on those measures give up their first queen fast.
The scale has nothing to do with maths or luck — every puzzle here is solvable by deduction and has exactly one answer. It measures reasoning depth: how many eliminations must stack up before a placement becomes provable. That depth is what separates a medium board from the rest.
When a board plays tougher than its label, look for a missed mark before you look for a clever deduction. Walk back over every queen you have placed and confirm the full row, the full column and all eight surrounding squares are crossed out. The diagonal neighbours are the ones players skip, and a single skipped diagonal will hide the next forced move indefinitely.
Techniques that work well at 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #177, start hunting for it near column 2.
Here is a shape check that gives nothing away: when #177 is solved, 4 queens sit on the outer edge of the grid and 8 sit inside it, and no queen lands in a corner. A work-in-progress board that clusters its queens in one quadrant while leaving others bare is usually carrying a mistake.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 12x12 Queens puzzle #177?
Puzzle #177 is rated medium. Its smallest color region holds 1 square, its tightest row is touched by 3 colors, and three of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #177 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #177, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #177?
Start with the sea green region — the most constrained color on this board, with 1 square spanning rows 10–10 and columns 4–4. Narrowing the smallest region first removes the most squares elsewhere on the grid.